Question: Evaluate the definite integral. $\int^{27}_{8}\left(\frac43\sqrt[3]{x}\right)\,dx = $
Solution: First, use the power rule: $\begin{aligned}\int^{27}_{8}\left(\frac43\sqrt[3]{x}\right)\,dx~&=~\int^{27}_{8}\left(\frac43x^\frac13\right)\,dx \\&=(x^\frac43)\Bigg|^{27}_{8}\end{aligned}$ Second, plug in the limits of integration: $[{27}^{\frac43}]-[8^{\frac43}] = 81-16 = 65$. The answer: $\int^{27}_{8}\left(\frac43\sqrt[3]{x}\right)\,dx~=~65$